61.34.15 problem 15

Internal problem ID [12779]
Book : Handbook of exact solutions for ordinary differential equations. By Polyanin and Zaitsev. Second edition
Section : Chapter 2, Second-Order Differential Equations. section 2.1.3-1. Equations with exponential functions
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 08:24:29 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+a \,{\mathrm e}^{\lambda x} y^{\prime }-b \,{\mathrm e}^{\mu x} \left (a \,{\mathrm e}^{\lambda x}+b \,{\mathrm e}^{\mu x}+\mu \right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 46

dsolve(diff(y(x),x$2)+a*exp(lambda*x)*diff(y(x),x)-b*exp(mu*x)*(a*exp(lambda*x)+b*exp(mu*x)+mu)*y(x)=0,y(x), singsol=all)
 

\[ y = \left (\left (\int {\mathrm e}^{\frac {-2 b \,{\mathrm e}^{\mu x} \lambda -{\mathrm e}^{\lambda x} a \mu }{\mu \lambda }}d x \right ) c_{1} +c_{2} \right ) {\mathrm e}^{\frac {b \,{\mathrm e}^{\mu x}}{\mu }} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}]+a*Exp[\[Lambda]*x]*D[y[x],x]-b*Exp[\[Mu]*x]*(a*Exp[\[Lambda]*x]+b*Exp[\[Mu]*x]+\[Mu])*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved